Question: Evaluate. $\left(\dfrac{1}{81}\right)^{^{\scriptsize\dfrac12}}\cdot\left(\dfrac{1}{81}\right)^{^{\scriptsize -\dfrac34}}=$
Solution: $\begin{aligned} \left(\dfrac{1}{81}\right)^{^{\scriptsize\dfrac12}}\cdot\left(\dfrac{1}{81}\right)^{^{\scriptsize -\dfrac34}}&=\left(\dfrac{1}{81}\right)^{^{\scriptsize\dfrac12+\left(-\dfrac34\right)}} \\\\ &=\left(\dfrac{1}{81}\right)^{^{\scriptsize\dfrac24-\dfrac34}} \\\\ &=\left(\dfrac{1}{81}\right)^{^{\scriptsize -\dfrac14}} \\\\ &=81^{^{\scriptsize\dfrac14}} \\\\ &=\sqrt[4]{81} \\\\ &=3 \end{aligned}$ In conclusion, $\left(\dfrac{1}{81}\right)^{^{\scriptsize\dfrac12}}\cdot\left(\dfrac{1}{81}\right)^{^{\scriptsize -\dfrac34}}=3$